When my '02 gets slow it's because hair has gotten caught on the drain closing mechanism. There should be a plastic nut under the sink on the back of the drain tube that, when removed along with the horizontal stem going through the drain plug, will allow the drain plug to be pulled up out of the sink. Then you will have access to the "hair ball". Fish out the mess, clean the drain, and reinstall the drain plug with the assembly with the nut through the hole in the end of the drain plug. Be aware that water can run out of the drain when this assembly is removed. (Wish I could have described this better)

Posts 2 and 3 should solve the problem. If not check the vent, but unlikely unless you can look up and see a problem at the top of the vent. BUT, if the trailer is under a tree, and leaves have fallen, the vent being compromised might rise up the list of possibilities IMO. [edit -- Assuming all other drains work OK]